Here is the derivation of the equations of motion by graphical method. Follow the graph:
Let us suppose that v 0 is the initial velocity of the particle, at time t = 0, and v be the velocity of the particle at t = t.
The acceleration a of the particle can be written as,
This is the 1 st kinematic equations for uniformly accelerated motion.
Suppose, the particle travels a distance x in the time t .
The area of blue colored part gives the distance covered x .
This is the 2 nd equation.
Now, for the 3 rd equation we shall modify the equation: